How T cell receptor (TCR) discriminates different peptides presented by the major histocompatibility complex molecule (pMHC) is a central question in adaptive immunity that defends humans against disease-causing pathogens. Yet its mechanism is poorly understood due at least partly to the lack of appropriate tools to analyze the initial recognition events at scales as small as single molecular interactions and as brief as subseconds, which are beyond the temporal and spatial resolutions of standard techniques. Adhesion frequency and thermal fluctuation assays - two techniques probing the first seconds of TCR/pMHC interactions - as well as two other single-bond methods (unbinding force and bond lifetime assays) will be used in the proposed research to study the dynamics of TCR/pMHC, CD8/MHC interactions and their crosstalk. Because of the inherent stochastic nature of single molecular interactions, statistical modeling approach is required for data analysis. Specifically, the data of three of the above assays are in the form of time series of binary adhesion scores or continuous values of unbinding forces or bond lifetimes with fixed intervals. The data of the thermal fluctuation assay are in the form of alternating bond lifetime and waiting time of random intervals. While some information can be obtained by using descriptive statistics, more sophisticated statistical modeling will enable us to greatly increase the understanding and utilities of the data. New class of time series models will be used to quantify the correlations of the adhesion scores, unbinding forces and bond lifetimes, which are manifested as memory effects, i.e., T cell's ability to remember the previous adhesion event and to alter the probability of occurrence and the probability densities of unbinding forces and lifetimes of the next adhesion event. Mixture distribution will be used to determine whether the measured single-bonds events consist of a homogeneous population of single states or a heterogeneous population of multi-state mixture. Change-point formulation will be employ for statistical estimation in the thermal fluctuation assay. These statistical models will be tested experimentally and modified as needed to extract the fundamental characteristics of TCR interaction with different peptides.